On Robustness in Optimization-Based Constrained Iterative Learning Control

TL;DR

This paper develops a robust optimization-based iterative learning control method for constrained linear systems, ensuring stability and constraint satisfaction despite uncertainties, with theoretical analysis and numerical validation.

Contribution

It introduces a forward-backward splitting algorithm for robust constrained ILC, integrating structured uncertainty for improved robustness and stability analysis.

Findings

Ensures constraint satisfaction under structured uncertainties.

Provides stability guarantees in the iteration domain.

Validated effectiveness through numerical simulations.

Abstract

Iterative learning control (ILC) is a control strategy for repetitive tasks wherein information from previous runs is leveraged to improve future performance. Optimization-based ILC (OB-ILC) is a powerful design framework for constrained ILC where measurements from the process are integrated into an optimization algorithm to provide robustness against noise and modelling error. This paper proposes a robust ILC controller for constrained linear processes based on the forward-backward splitting algorithm. It demonstrates how structured uncertainty information can be leveraged to ensure constraint satisfaction and provides a rigorous stability analysis in the iteration domain by combining concepts from monotone operator theory and robust control. Numerical simulations of a precision motion stage support the theoretical results.